179 — Solucionario Calculo Una Variable Thomas Finney Edicion 9

Discarding the trivial solution (x = 0) (which gave zero volume), she solved

When she stood, the room fell silent. She described the geometry, the substitution of , the elegant reduction to a single‑variable function, and the calculus steps that led to the cube. She finished with the final expression (\displaystyle V_{\max}= \frac{8R^3}{3\sqrt{3}}) and a quick sketch of the inscribed cube inside the sphere. Discarding the trivial solution (x = 0) (which

Maya solved for in terms of x :

Plugging this back into the expression for : Maya solved for in terms of x :

A ripple of impressed murmurs ran through the class. The professor nodded, his eyes twinkling. “Excellent,” he said. “You’ve illustrated perfectly how a multivariable problem can sometimes be reduced to one variable, and how the critical point tells us the shape of the optimal object. Well done, Maya.” his eyes twinkling. “Excellent